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A certain academic department consists of 3 senior professors and 6 ju
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04 Oct 2021, 08:56
04 Oct 2021, 08:56
Expert Reply
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Question Stats:
71% (01:10) correct
28% (02:07) wrong based on 14 sessions
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A certain academic department consists of 3 senior professors and 6 junior professors. How many different committees of 3 professors can be formed in which at least one member of the committee is a senior professor? (Two groups are considered different if at least one group member is different.)
(A) 168
(B) 127
(C) 66
(D) 64
(E) 36
(A) 168
(B) 127
(C) 66
(D) 64
(E) 36
Re: A certain academic department consists of 3 senior professors and 6 ju
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04 Oct 2021, 20:10
04 Oct 2021, 20:10
1
The problems with atleast can be calculated as Total - none
We have \(3\) senior professors and \(6\) junior professors.
Total 9 prof. from which a committee of \(3\)
Total com. can be formed \(= 9\)C\(3 = 84\)
Let's consider when no senior professors are taken in the committee.
Total com. from \(6\) junior prof \(= 6\)C\(3 = 20\)
Hence, the no of committees when we will have at least \(1\) senior professor \(= 84 - 20 = 64\)
Answer D
We have \(3\) senior professors and \(6\) junior professors.
Total 9 prof. from which a committee of \(3\)
Total com. can be formed \(= 9\)C\(3 = 84\)
Let's consider when no senior professors are taken in the committee.
Total com. from \(6\) junior prof \(= 6\)C\(3 = 20\)
Hence, the no of committees when we will have at least \(1\) senior professor \(= 84 - 20 = 64\)
Answer D
Re: A certain academic department consists of 3 senior professors and 6 ju
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11 Jul 2022, 21:56
11 Jul 2022, 21:56
1
Way #2
Atleast one senior professor should be there,
--- atleast 1 equals more than or equal to 1 ---- in this case either 1 or 2 or 3. (since only 3 member community is to be formed).
We have 3 senior professors (S) and 6 junior professors (J).
1. 2 J + 1 S = 6c2 x 3c1 = 15 x 3 = 45
2. 1 J + 2 S = 6c1 x 3c2 = 6 x 3 = 18
3. 0 J + 3 S = 6c0 x 3c3 = 1 x 1 = 1
Total group can be formed = 45 +18 1 = 64
Answer D
_________________
Atleast one senior professor should be there,
--- atleast 1 equals more than or equal to 1 ---- in this case either 1 or 2 or 3. (since only 3 member community is to be formed).
We have 3 senior professors (S) and 6 junior professors (J).
1. 2 J + 1 S = 6c2 x 3c1 = 15 x 3 = 45
2. 1 J + 2 S = 6c1 x 3c2 = 6 x 3 = 18
3. 0 J + 3 S = 6c0 x 3c3 = 1 x 1 = 1
Total group can be formed = 45 +18 1 = 64
Answer D
_________________
